https://file.aiquickdraw.com/mathbot/file/1726985491835sakv3hgc.jpg

To solve the problem from the image:

We are given:
- \( P(A) = 0.64 \)
- \( P(A \text{ and } B) = 0.12 \)

We need to find \( P(B) \). Since \( A \) and \( B \) are independent events, the following formula applies:

\[
P(A \text{ and } B) = P(A) \times P(B)
\]

Now, we can solve for \( P(B) \):

\[
P(B) = \frac{P(A \text{ and } B)}{P(A)} = \frac{0.12}{0.64}
\]

Let me calculate that for you.

The probability \( P(B) \) is \( 0.1875 \).

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What does it mean for two events to be independent?
2. How would you calculate \( P(A \text{ or } B) \) if events A and B were mutually exclusive?
3. If \( P(A) = 0.64 \) and \( P(B) = 0.1875 \), what is \( P(A \cup B) \) for independent events?
4. How does conditional probability differ from independent probability?
5. How would this problem change if \( A \) and \( B \) were dependent events?

**Tip:** For independent events, the occurrence of one does not affect the probability of the other happening.

A and B are independent events. Given P(A) = 0.64 and P(A and B) = 0.12, find P(B).

In this probability problem, you'll learn how to calculate the probability of independent events. Given P(A) = 0.64 and P(A and B) = 0.12, the solution demonstrates how to find P(B) using the multiplication rule for independent events. Suitable for Grades 9-12.

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